Comparison Between Roe's Scheme and Cell-centered scheme For Transonic Flow Pass Through a Turbine Blades Section

Abstract

The finite volume method (FVM) is a discretization technique for partial differential equations, especially those that arise from physical conservation laws. FVM uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations [1]. The present work employs the Cell- centred and Roe's scheme to investigate the inviscid compressible flow pass through a two dimensional blade on two types of blade shapes: Blazek and SE1050 blade models. The governing equation of fluid motion of the flow problem in hand is the Euler Equation. The behavior of this equation will depend on the local Mach number if the governing equation stated in the form as the governing equation of steady flow problem. If the local Mach number is less than one, the governing equation will behave as elliptic type of differential equation while if the Mach number is greater than one it will behave as hyperbolic type of differential equation. Elimination of the presence of those two types governing equation for the case of transonic flow problem can be achieved by representing the Euler equation in unsteady form. So the equation becomes hyperbolic with respect to time. There are various Finite Volume Methods that can used for solving hyperbolic type of equation, such as Cell-centered scheme [2], Roe Upwind Scheme [3] and TVD Scheme [1]. Those computer codes apply in the case of inviscid two dimensional compressible flow pass through blades of turbine. The present work focuses on two computer codes, first based on Cell Centre scheme and the second one based on Roe's scheme.